Regular Spherical (n=1, 2, 3, ...) |
Article | Vertex configuration | Schläfli symbol | Image |
Dihedron |
n2 |
{n,2} |
{6,2} |
Hosohedron |
2n |
{2,n} |
{2,6} |
Spherical tetrahedron |
33 |
{3,3} |
|
Spherical octahedron |
34 |
{3,4} |
|
Spherical cube |
43 |
{4,3} |
|
Spherical icosahedron |
35 |
{3,5} |
|
Spherical dodecahedron |
53 |
{5,3} |
|
Semi-regular |
Article | Vertex configuration | Schläfli symbol | Image |
Apeirogonal prism |
42.∞ |
t{2,∞} |
|
Apeirogonal antiprism |
33.∞ |
sr{2,∞} |
|
Snub square tiling |
32.4.3.4 |
s{4,4} |
|
Elongated triangular tiling |
33.42 |
{3,6}:e |
|
Snub trihexagonal tiling |
34.6 |
sr{6,3} |
|
Rhombitrihexagonal tiling |
3.4.6.4 |
rr{6,3} |
|
Trihexagonal tiling |
3.6.3.6 |
r{6,3} |
|
Truncated hexagonal tiling |
3.122 |
t{6,3} |
|
Truncated trihexagonal tiling |
4.6.12 |
tr{6,3} |
|
Truncated square tiling |
4.82 |
tr{4,4} |
|
Dual semi-regular |
Article | Face configuration | Schläfli symbol | Image |
Apeirogonal deltohedron |
V33.∞ |
dsr{2,∞} |
|
Apeirogonal bipyramid |
V42.∞ |
dt{2,∞} |
|
Cairo pentagonal tiling |
V32.4.3.4 |
ds{4,4} |
|
Prismatic pentagonal tiling |
V33.42 |
d{3,6}:e |
|
Floret pentagonal tiling |
V34.6 |
dsr{6,3} |
|
Deltoidal trihexagonal tiling |
V3.4.6.4 |
drr{6,3} |
|
Rhombille tiling |
V3.6.3.6 |
dr{6,3} |
|
Triakis triangular tiling |
V3.122 |
dt{6,3} |
|
Kisrhombille tiling |
V4.6.12 |
dtr{6,3} |
|
Tetrakis square tiling |
4.82 |
tr{4,4} |
|
|
Hyperbolic |
Article | Vertex configuration | Schläfli symbol | Image |
Snub tetrapentagonal tiling |
32.4.3.5 |
sr{5,4} |
|
Snub tetrahexagonal tiling |
32.4.3.6 |
sr{6,4} |
|
Snub tetraheptagonal tiling |
32.4.3.7 |
sr{7,4} |
|
Snub tetraoctagonal tiling |
32.4.3.8 |
sr{8,4} |
|
Snub tetraapeirogonal tiling |
32.4.3.∞ |
sr{∞,4} |
|
Snub pentapentagonal tiling |
32.5.3.5 |
s{5,4} |
|
Snub pentahexagonal tiling |
32.5.3.6 |
sr{6,5} |
|
Snub hexahexagonal tiling |
32.6.3.6 |
s{6,4} |
|
Snub hexaoctagonal tiling |
32.6.3.8 |
sr{8,6} |
|
Snub heptaheptagonal tiling |
32.7.3.7 |
sr{7,7} |
|
Snub octaoctagonal tiling |
32.8.3.8 |
s{8,4} |
|
Snub order-6 square tiling |
33.4.3.4 |
s{4,6} |
|
Snub apeiroapeirogonal tiling |
32.∞.3.∞ |
sr{∞,∞} |
|
Snub triheptagonal tiling |
34.7 |
sr{7,3} |
|
Snub trioctagonal tiling |
34.8 |
sr{8,3} |
|
Snub triapeirogonal tiling |
34.∞ |
sr{∞,3} |
|
Snub order-8 triangular tiling |
35.4 |
s{3,8} |
|
Order-7 triangular tiling |
37 |
{3,7} |
|
Order-8 triangular tiling |
38 |
{3,8} |
|
Infinite-order triangular tiling |
3∞ |
{3,∞} |
|
Alternated octagonal tiling |
3.4.3.4.3.4 |
h{8,3} |
|
Alternated order-4 hexagonal tiling |
3.4.3.4.3.4.3.4 |
h{6,4} |
|
Quarter order-6 square tiling |
3.4.62.4 |
q{4,6} |
|
Rhombitriheptagonal tiling |
3.4.7.4 |
rr{7,3} |
|
Rhombitrioctagonal tiling |
3.4.8.4 |
rr{8,3} |
|
Rhombitriapeirogonal tiling |
3.4.∞.4 |
rr{∞,3} |
|
Cantic octagonal tiling |
3.6.4.6 |
h2{8,3} |
|
Triheptagonal tiling |
3.7.3.7 |
r{7,3} |
|
Trioctagonal tiling |
3.8.3.8 |
r{8,3} |
|
Truncated heptagonal tiling |
3.142 |
t{7,3} |
|
Truncated octagonal tiling |
3.162 |
t{8,3} |
|
Triapeirogonal tiling |
3.∞.3.∞ |
r{∞,3} |
|
Truncated order-3 apeirogonal tiling |
3.∞2 |
t{∞,3} |
|
Rhombitetrapentagonal tiling |
42.5.4 |
rr{5,4} |
|
Rhombitetrahexagonal tiling |
42.6.4 |
rr{6,4} |
|
Rhombitetraheptagonal tiling |
42.7.4 |
rr{7,4} |
|
Rhombitetraoctagonal tiling |
42.8.4 |
rr{8,4} |
|
Rhombitetraapeirogonal tiling |
42.∞.4 |
rr{∞,4} |
|
Order-5 square tiling |
45 |
{4,5} |
|
Order-6 square tiling |
46 |
{4,6} |
|
Order-7 square tiling |
47 |
{4,7} |
|
Order-8 square tiling |
48 |
{4,8} |
|
Infinite-order square tiling |
4∞ |
{4,∞} |
|
Tetrapentagonal tiling |
4.5.4.5 |
r{5,4} |
|
Tetrahexagonal tiling |
4.6.4.6 |
r{6,4} |
|
Truncated trihexagonal tiling |
4.6.12 |
tr{6,3} |
|
Truncated triheptagonal tiling |
4.6.14 |
tr{7,3} |
|
Order 3-7 kisrhombille |
V4.6.14 |
??? |
|
Truncated trioctagonal tiling |
4.6.16 |
tr{8,3} |
|
Order 3-8 kisrhombille |
V4.6.16 |
??? |
|
Truncated triapeirogonal tiling |
4.6.∞ |
tr{∞,3} |
|
Tetraheptagonal tiling |
4.7.4.7 |
r{7,4} |
|
Tetraoctagonal tiling |
4.8.4.8 |
r{8,4} |
|
Truncated tetrapentagonal tiling |
4.8.10 |
tr{5,4} |
|
4-5 kisrhombille |
V4.8.10 |
??? |
|
Truncated tetrahexagonal tiling |
4.8.12 |
tr{6,4} |
|
Truncated tetraheptagonal tiling |
4.8.14 |
tr{7,4} |
|
Truncated tetraoctagonal tiling |
4.8.16 |
tr{8,4} |
|
Truncated tetraapeirogonal tiling |
4.8.∞ |
tr{∞,4} |
|
Truncated order-4 pentagonal tiling |
4.102 |
t{5,4} |
|
Truncated pentahexagonal tiling |
4.10.12 |
tr{6,5} |
|
Truncated order-4 hexagonal tiling |
4.122 |
t{6,4} |
|
Truncated hexaoctagonal tiling |
4.12.16 |
tr{8,6} |
|
Truncated order-4 heptagonal tiling |
4.142 |
t{7,4} |
|
Truncated order-4 octagonal tiling |
4.162 |
t{8,4} |
|
Truncated order-4 apeirogonal tiling |
4.∞2 |
t{∞,4} |
|
Tetraapeirogonal tiling |
4.∞.4.∞ |
r{∞,4} |
|
Order-4 pentagonal tiling |
54 |
{5,4} |
|
Order-5 pentagonal tiling |
55 |
{5,5} |
|
Order-6 pentagonal tiling |
56 |
{5,6} |
|
Infinite-order pentagonal tiling |
5∞ |
{5,∞} |
|
Rhombipentahexagonal tiling |
5.4.6.4 |
rr{6,5} |
|
Pentahexagonal tiling |
5.6.5.6 |
r{6,5} |
|
Truncated order-5 square tiling |
5.82 |
t{4,5} |
|
Truncated order-5 pentagonal tiling |
5.102 |
t{5,5} |
|
Truncated order-5 hexagonal tiling |
5.122 |
t{6,5} |
|
Pentaapeirogonal tiling |
5.∞.5.∞ |
r{∞,5} |
|
Order-4 hexagonal tiling |
64 |
{6,4} |
|
Order-5 hexagonal tiling |
65 |
{6,5} |
|
Order-6 hexagonal tiling |
66 |
{6,6} |
|
Order-8 hexagonal tiling |
68 |
{6,8} |
|
Rhombihexaoctagonal tiling |
6.4.8.4 |
rr{8,6} |
|
Hexaoctagonal tiling |
6.8.6.8 |
r{8,6} |
|
Truncated order-6 square tiling |
6.82 |
t{4,6} |
|
Truncated order-6 pentagonal tiling |
6.102 |
t{5,6} |
|
Truncated order-6 hexagonal tiling |
6.122 |
t{6,6} |
|
Truncated order-6 octagonal tiling |
6.162 |
t{8,6} |
|
Heptagonal tiling |
73 |
{7,3} |
|
Order-4 heptagonal tiling |
74 |
{7,4} |
|
Order-7 heptagonal tiling |
77 |
{7,7} |
|
Truncated order-7 triangular tiling |
7.62 |
t{3,7} |
|
Truncated order-7 square tiling |
7.82 |
t{4,7} |
|
Truncated order-7 heptagonal tiling |
7.142 |
t{7,7} |
|
Octagonal tiling |
83 |
{8,3} |
|
Order-4 octagonal tiling |
84 |
{8,4} |
|
Order-6 octagonal tiling |
86 |
{8,6} |
|
Order-8 octagonal tiling |
88 |
{8,8} |
|
Truncated order-8 hexagonal tiling |
812 |
t{6,8} |
|
Truncated order-8 triangular tiling |
8.62 |
t{3,8} |
|
Truncated order-8 octagonal tiling |
8.162 |
t{8,8} |
|
Order-7 heptagrammic tiling |
(7/2)7 |
{7/2,7} |
|
Order-3 apeirogonal tiling |
∞3 |
{∞,3} |
|
Order-4 apeirogonal tiling |
∞4 |
{∞,4} |
|
Order-5 apeirogonal tiling |
∞5 |
{∞,5} |
|
Infinite-order apeirogonal tiling |
∞∞ |
{∞,∞} |
|
Truncated infinite-order triangular tiling |
∞.62 |
t{3,∞} |
|
Truncated infinite-order square tiling |
∞.82 |
t{4,∞} |
|
|